Abstract

We introduce a technique for simultaneously measuring the time-dependent intensity and phase of two independent and arbitrary ultrashort laser pulses from a single measured spectrogram. This two-pulse method is mathematically equivalent to the problem of blind deconvolution, and we use an algorithm analogous to those used for deblurring two-dimensional images to recover the two pulses. We demonstrate the method by simultaneously retrieving the intensity and the phase of two different pulses from a Ti:sapphire laser, one of which is chirped by propagation through glass.

© 1995 Optical Society of America

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  1. A. Freiberg and P. Saari, "Picosecond spectrochronography," IEEE J. Quantum Electron. QE-19, 622–630 (1983).
    [CrossRef]
  2. M. Mycek, S. Weiss, J. Bigot, S. Schmitt-Rink, and D. S. Chemla, "Femtosecond time-resolved free-induction decay of room-temperature exitons in GaAs quantum wells," Appl. Phys. Lett. 60, 2666–2668 (1992).
    [CrossRef]
  3. V. G. Lyssenko, J. Erland, I. Balslev, K.-H. Pantke, B. S. Razbirin, and J. M. Hvam, "Nature of nonlinear four-wave-mixing beats in semiconductors," Phys. Rev. B 48, 5720–5723 (1993).
    [CrossRef]
  4. J.-Y. Bigot, M.-A. Mycek, S. Weiss, R. G. Ulbrich, and D. S. Chemla, "Instantaneous frequency dynamics of coherent wave mixing in semiconductor quantum wells," Phys. Rev. Lett. 70, 3307–3310 (1993).
    [CrossRef] [PubMed]
  5. D. J. Kane and R. Trebino, "Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical gating," Opt. Lett. 18, 823–825 (1993).
    [CrossRef] [PubMed]
  6. J. L. A. Chilla and O. E. Martinez, "Direct determination of the amplitude and the phase of femtosecond light pulses," Opt. Lett. 16, 39–41 (1991).
    [CrossRef] [PubMed]
  7. K. C. Chu, J. P. Heritage, R. S. Grant, K. X. Liu, A. Dienes, W. E. White, and A. Sullivan, "Direct measurement of the spectral phase of femtosecond pulses," Opt. Lett. 20, 904–906 (1995).
    [CrossRef] [PubMed]
  8. B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, "A simple method for the determination of the intensity and phase of ultrashort optical pulses," Opt. Commun. 113, 79–84 (1995).
    [CrossRef]
  9. R. Trebino and D. J. Kane, "Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating," J. Opt. Soc. Am. A 10, 1101–1111 (1993).
    [CrossRef]
  10. K. W. DeLong, R. Trebino, and D. J. Kane, "A comparison of ultrashort-pulse frequency-resolved-optical-gating traces for three common beam geometries," J. Opt. Soc. Am. B 11, 1595–1608 (1994).
    [CrossRef]
  11. J. Paye, M. Ramaswamy, J. G. Fujimoto, and E. P. Ippen, "Measurement of the amplitude and phase of ultrashort light pulses from spectrally resolved autocorrelation," Opt. Lett. 18, 1946–1948 (1993).
    [CrossRef] [PubMed]
  12. J. Paye, "The chronocyclic representation of ultrashort light pulses," IEEE J. Quantum Electron. 28, 2262–2273 (1992).
    [CrossRef]
  13. B. C. McCallum and J. M. Rodenburg, "Simultaneous reconstruction of object and aperture functions from multiple far-field intensity measurements," J. Opt. Soc. Am. A 10, 231–239 (1993).
    [CrossRef]
  14. G. R. Ayers and J. C. Dainty, "Iterative blind deconvolution method and its applications," Opt. Lett. 13, 547–549 (1988).
    [CrossRef] [PubMed]
  15. K. W. DeLong and R. Trebino, "Measuring the intensity and phase of two ultrashort pulses on a single shot," in Generation, Amplification, and Measurement of Ultrashort Laser Pulses, R. P. Trebino and I. A. Walmsleys, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2116,268–274 (1994).
    [CrossRef]
  16. Y. Ishida, K. Naganuma, and T. Yajima, "Self-phase modulation in hybridly mode-locked CW dye lasers," IEEE J. Quantum Electron. 21, 69–77 (1985).
    [CrossRef]
  17. K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, "Frequency-resolved optical gating using second-harmonic generation," J. Opt. Soc. Am. B 11, 2206–2215 (1994).
    [CrossRef]
  18. J. H. Seldin and J. R. Fienup, "Interative blind deconvolution algorithm applied to phase retrieval," J. Opt. Soc. Am. A 7, 428–433 (1990).
    [CrossRef]
  19. A. Levi and H. Stark, Image Recovery: Theory and Applications, H. Stark, ed. (Academic, San Diego, 1987), pp. 277–320.
  20. K. W. DeLong, D. N. Fittinghoff, R. Trebino, B. Kohler, and K. Wilson, "Pulse retrieval in frequency-resolved optical gating using the method of generalized projections," Opt. Lett. 19, 2152–2154 (1994).
    [CrossRef] [PubMed]
  21. Y. Yang, N. P. Galatsanos, and H. Stark, "Projection-based blind deconvolution," J. Opt. Soc. Am. A 11, 2401–2409 (1994).
    [CrossRef]
  22. In particular, pairs of linearly chirped Gaussian pulses exhibit ambiguities without the spectral constraint. It is unknown whether these ambiguities represent a general feature of TREEFROG or occur only for these pulses.
  23. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, 1989), p. 8.
  24. Schott Computer Glass Catalog 1.0, Schott Glasswerke, Mainz, Germany, 1992.
  25. D. N. Fittinghoff, K. W. DeLong, R. Trebino, and C. L. Ladera, "Noise sensitivity in frequency-resolved optical gating measurements of ultrashort pulses," J. Opt. Soc. Am. B 12, 1955–1967 (1995).
    [CrossRef]

1995 (3)

1994 (4)

1993 (6)

1992 (2)

M. Mycek, S. Weiss, J. Bigot, S. Schmitt-Rink, and D. S. Chemla, "Femtosecond time-resolved free-induction decay of room-temperature exitons in GaAs quantum wells," Appl. Phys. Lett. 60, 2666–2668 (1992).
[CrossRef]

J. Paye, "The chronocyclic representation of ultrashort light pulses," IEEE J. Quantum Electron. 28, 2262–2273 (1992).
[CrossRef]

1991 (1)

1990 (1)

1988 (1)

1985 (1)

Y. Ishida, K. Naganuma, and T. Yajima, "Self-phase modulation in hybridly mode-locked CW dye lasers," IEEE J. Quantum Electron. 21, 69–77 (1985).
[CrossRef]

1983 (1)

A. Freiberg and P. Saari, "Picosecond spectrochronography," IEEE J. Quantum Electron. QE-19, 622–630 (1983).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, 1989), p. 8.

Ayers, G. R.

Balslev, I.

V. G. Lyssenko, J. Erland, I. Balslev, K.-H. Pantke, B. S. Razbirin, and J. M. Hvam, "Nature of nonlinear four-wave-mixing beats in semiconductors," Phys. Rev. B 48, 5720–5723 (1993).
[CrossRef]

Bigot, J.

M. Mycek, S. Weiss, J. Bigot, S. Schmitt-Rink, and D. S. Chemla, "Femtosecond time-resolved free-induction decay of room-temperature exitons in GaAs quantum wells," Appl. Phys. Lett. 60, 2666–2668 (1992).
[CrossRef]

Bigot, J.-Y.

J.-Y. Bigot, M.-A. Mycek, S. Weiss, R. G. Ulbrich, and D. S. Chemla, "Instantaneous frequency dynamics of coherent wave mixing in semiconductor quantum wells," Phys. Rev. Lett. 70, 3307–3310 (1993).
[CrossRef] [PubMed]

Chemla, D. S.

J.-Y. Bigot, M.-A. Mycek, S. Weiss, R. G. Ulbrich, and D. S. Chemla, "Instantaneous frequency dynamics of coherent wave mixing in semiconductor quantum wells," Phys. Rev. Lett. 70, 3307–3310 (1993).
[CrossRef] [PubMed]

M. Mycek, S. Weiss, J. Bigot, S. Schmitt-Rink, and D. S. Chemla, "Femtosecond time-resolved free-induction decay of room-temperature exitons in GaAs quantum wells," Appl. Phys. Lett. 60, 2666–2668 (1992).
[CrossRef]

Chilla, J. L. A.

Chu, K. C.

Dainty, J. C.

DeLong, K. W.

Dienes, A.

Erland, J.

V. G. Lyssenko, J. Erland, I. Balslev, K.-H. Pantke, B. S. Razbirin, and J. M. Hvam, "Nature of nonlinear four-wave-mixing beats in semiconductors," Phys. Rev. B 48, 5720–5723 (1993).
[CrossRef]

Fienup, J. R.

Fittinghoff, D. N.

Franco, M. A.

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, "A simple method for the determination of the intensity and phase of ultrashort optical pulses," Opt. Commun. 113, 79–84 (1995).
[CrossRef]

Freiberg, A.

A. Freiberg and P. Saari, "Picosecond spectrochronography," IEEE J. Quantum Electron. QE-19, 622–630 (1983).
[CrossRef]

Fujimoto, J. G.

Galatsanos, N. P.

Grant, R. S.

Heritage, J. P.

Hunter, J.

Hvam, J. M.

V. G. Lyssenko, J. Erland, I. Balslev, K.-H. Pantke, B. S. Razbirin, and J. M. Hvam, "Nature of nonlinear four-wave-mixing beats in semiconductors," Phys. Rev. B 48, 5720–5723 (1993).
[CrossRef]

Ippen, E. P.

Ishida, Y.

Y. Ishida, K. Naganuma, and T. Yajima, "Self-phase modulation in hybridly mode-locked CW dye lasers," IEEE J. Quantum Electron. 21, 69–77 (1985).
[CrossRef]

Kane, D. J.

Kohler, B.

Ladera, C. L.

Levi, A.

A. Levi and H. Stark, Image Recovery: Theory and Applications, H. Stark, ed. (Academic, San Diego, 1987), pp. 277–320.

Liu, K. X.

Lyssenko, V. G.

V. G. Lyssenko, J. Erland, I. Balslev, K.-H. Pantke, B. S. Razbirin, and J. M. Hvam, "Nature of nonlinear four-wave-mixing beats in semiconductors," Phys. Rev. B 48, 5720–5723 (1993).
[CrossRef]

Martinez, O. E.

McCallum, B. C.

Mycek, M.

M. Mycek, S. Weiss, J. Bigot, S. Schmitt-Rink, and D. S. Chemla, "Femtosecond time-resolved free-induction decay of room-temperature exitons in GaAs quantum wells," Appl. Phys. Lett. 60, 2666–2668 (1992).
[CrossRef]

Mycek, M.-A.

J.-Y. Bigot, M.-A. Mycek, S. Weiss, R. G. Ulbrich, and D. S. Chemla, "Instantaneous frequency dynamics of coherent wave mixing in semiconductor quantum wells," Phys. Rev. Lett. 70, 3307–3310 (1993).
[CrossRef] [PubMed]

Mysyrowicz, A.

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, "A simple method for the determination of the intensity and phase of ultrashort optical pulses," Opt. Commun. 113, 79–84 (1995).
[CrossRef]

Naganuma, K.

Y. Ishida, K. Naganuma, and T. Yajima, "Self-phase modulation in hybridly mode-locked CW dye lasers," IEEE J. Quantum Electron. 21, 69–77 (1985).
[CrossRef]

Nibbering, E. T. J.

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, "A simple method for the determination of the intensity and phase of ultrashort optical pulses," Opt. Commun. 113, 79–84 (1995).
[CrossRef]

Pantke, K.-H.

V. G. Lyssenko, J. Erland, I. Balslev, K.-H. Pantke, B. S. Razbirin, and J. M. Hvam, "Nature of nonlinear four-wave-mixing beats in semiconductors," Phys. Rev. B 48, 5720–5723 (1993).
[CrossRef]

Paye, J.

Prade, B. S.

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, "A simple method for the determination of the intensity and phase of ultrashort optical pulses," Opt. Commun. 113, 79–84 (1995).
[CrossRef]

Ramaswamy, M.

Razbirin, B. S.

V. G. Lyssenko, J. Erland, I. Balslev, K.-H. Pantke, B. S. Razbirin, and J. M. Hvam, "Nature of nonlinear four-wave-mixing beats in semiconductors," Phys. Rev. B 48, 5720–5723 (1993).
[CrossRef]

Rodenburg, J. M.

Saari, P.

A. Freiberg and P. Saari, "Picosecond spectrochronography," IEEE J. Quantum Electron. QE-19, 622–630 (1983).
[CrossRef]

Schins, J. M.

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, "A simple method for the determination of the intensity and phase of ultrashort optical pulses," Opt. Commun. 113, 79–84 (1995).
[CrossRef]

Schmitt-Rink, S.

M. Mycek, S. Weiss, J. Bigot, S. Schmitt-Rink, and D. S. Chemla, "Femtosecond time-resolved free-induction decay of room-temperature exitons in GaAs quantum wells," Appl. Phys. Lett. 60, 2666–2668 (1992).
[CrossRef]

Seldin, J. H.

Stark, H.

Y. Yang, N. P. Galatsanos, and H. Stark, "Projection-based blind deconvolution," J. Opt. Soc. Am. A 11, 2401–2409 (1994).
[CrossRef]

A. Levi and H. Stark, Image Recovery: Theory and Applications, H. Stark, ed. (Academic, San Diego, 1987), pp. 277–320.

Sullivan, A.

Trebino, R.

D. N. Fittinghoff, K. W. DeLong, R. Trebino, and C. L. Ladera, "Noise sensitivity in frequency-resolved optical gating measurements of ultrashort pulses," J. Opt. Soc. Am. B 12, 1955–1967 (1995).
[CrossRef]

K. W. DeLong, D. N. Fittinghoff, R. Trebino, B. Kohler, and K. Wilson, "Pulse retrieval in frequency-resolved optical gating using the method of generalized projections," Opt. Lett. 19, 2152–2154 (1994).
[CrossRef] [PubMed]

K. W. DeLong, R. Trebino, and D. J. Kane, "A comparison of ultrashort-pulse frequency-resolved-optical-gating traces for three common beam geometries," J. Opt. Soc. Am. B 11, 1595–1608 (1994).
[CrossRef]

K. W. DeLong, R. Trebino, J. Hunter, and W. E. White, "Frequency-resolved optical gating using second-harmonic generation," J. Opt. Soc. Am. B 11, 2206–2215 (1994).
[CrossRef]

R. Trebino and D. J. Kane, "Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating," J. Opt. Soc. Am. A 10, 1101–1111 (1993).
[CrossRef]

D. J. Kane and R. Trebino, "Single-shot measurement of the intensity and phase of an arbitrary ultrashort pulse by using frequency-resolved optical gating," Opt. Lett. 18, 823–825 (1993).
[CrossRef] [PubMed]

K. W. DeLong and R. Trebino, "Measuring the intensity and phase of two ultrashort pulses on a single shot," in Generation, Amplification, and Measurement of Ultrashort Laser Pulses, R. P. Trebino and I. A. Walmsleys, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2116,268–274 (1994).
[CrossRef]

Ulbrich, R. G.

J.-Y. Bigot, M.-A. Mycek, S. Weiss, R. G. Ulbrich, and D. S. Chemla, "Instantaneous frequency dynamics of coherent wave mixing in semiconductor quantum wells," Phys. Rev. Lett. 70, 3307–3310 (1993).
[CrossRef] [PubMed]

Weiss, S.

J.-Y. Bigot, M.-A. Mycek, S. Weiss, R. G. Ulbrich, and D. S. Chemla, "Instantaneous frequency dynamics of coherent wave mixing in semiconductor quantum wells," Phys. Rev. Lett. 70, 3307–3310 (1993).
[CrossRef] [PubMed]

M. Mycek, S. Weiss, J. Bigot, S. Schmitt-Rink, and D. S. Chemla, "Femtosecond time-resolved free-induction decay of room-temperature exitons in GaAs quantum wells," Appl. Phys. Lett. 60, 2666–2668 (1992).
[CrossRef]

White, W. E.

Wilson, K.

Yajima, T.

Y. Ishida, K. Naganuma, and T. Yajima, "Self-phase modulation in hybridly mode-locked CW dye lasers," IEEE J. Quantum Electron. 21, 69–77 (1985).
[CrossRef]

Yang, Y.

Appl. Phys. Lett. (1)

M. Mycek, S. Weiss, J. Bigot, S. Schmitt-Rink, and D. S. Chemla, "Femtosecond time-resolved free-induction decay of room-temperature exitons in GaAs quantum wells," Appl. Phys. Lett. 60, 2666–2668 (1992).
[CrossRef]

IEEE J. Quantum Electron. (3)

A. Freiberg and P. Saari, "Picosecond spectrochronography," IEEE J. Quantum Electron. QE-19, 622–630 (1983).
[CrossRef]

Y. Ishida, K. Naganuma, and T. Yajima, "Self-phase modulation in hybridly mode-locked CW dye lasers," IEEE J. Quantum Electron. 21, 69–77 (1985).
[CrossRef]

J. Paye, "The chronocyclic representation of ultrashort light pulses," IEEE J. Quantum Electron. 28, 2262–2273 (1992).
[CrossRef]

J. Opt. Soc. Am. A (4)

J. Opt. Soc. Am. B (3)

Opt. Commun. (1)

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, "A simple method for the determination of the intensity and phase of ultrashort optical pulses," Opt. Commun. 113, 79–84 (1995).
[CrossRef]

Opt. Lett. (6)

Phys. Rev. B (1)

V. G. Lyssenko, J. Erland, I. Balslev, K.-H. Pantke, B. S. Razbirin, and J. M. Hvam, "Nature of nonlinear four-wave-mixing beats in semiconductors," Phys. Rev. B 48, 5720–5723 (1993).
[CrossRef]

Phys. Rev. Lett. (1)

J.-Y. Bigot, M.-A. Mycek, S. Weiss, R. G. Ulbrich, and D. S. Chemla, "Instantaneous frequency dynamics of coherent wave mixing in semiconductor quantum wells," Phys. Rev. Lett. 70, 3307–3310 (1993).
[CrossRef] [PubMed]

Other (5)

A. Levi and H. Stark, Image Recovery: Theory and Applications, H. Stark, ed. (Academic, San Diego, 1987), pp. 277–320.

In particular, pairs of linearly chirped Gaussian pulses exhibit ambiguities without the spectral constraint. It is unknown whether these ambiguities represent a general feature of TREEFROG or occur only for these pulses.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, 1989), p. 8.

Schott Computer Glass Catalog 1.0, Schott Glasswerke, Mainz, Germany, 1992.

K. W. DeLong and R. Trebino, "Measuring the intensity and phase of two ultrashort pulses on a single shot," in Generation, Amplification, and Measurement of Ultrashort Laser Pulses, R. P. Trebino and I. A. Walmsleys, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2116,268–274 (1994).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Second-harmonic generation TREEFROG traces generated by a probe with temporal cubic phase and an unchirped gate. Both pulses have a Gaussian intensity profile and were calculated on a 64-element array. The probe has a full-width at half-maximum of 10, and the gate has a width of (a) 4, (b) 8, (c) 16. As the gate gets smaller, its spectral content increases, so that the TREEFROG trace gets wider in the spectral dimension. The longer gate pulse (c), with its narrow spectrum, resolves spectral oscillations that are washed out in the traces made with shorter gate pulses.

Fig. 2
Fig. 2

Experimental arrangement for SHG TREEFROG. The probe pulse is chirped by propagation through 6.5 cm of BK7 glass. The cross-correlation signal generated through SHG is frequency resolved to yield the TREEFROG trace.

Fig. 3
Fig. 3

Experimentally measured TREEFROG trace.

Fig. 4
Fig. 4

Fields of the (a) probe and (b) gate retrieved by the use of TREEFROG compared with the fields retrieved by the use of standard SHG FROG. The agreement is quite good.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

E sig ( t , τ ) = P ( t ) G ( t - τ ) .
I TREEFROG ( ω , τ ) = | - d t E sig ( t , τ ) exp ( i ω t ) | 2 .
Z = t , τ = 1 N E sig ( t , τ ) - P ( t ) G ( t - τ ) 2 .

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